Portfolio risk measurement under the nested setting is a challenging computational problem, and has received increasing attention in recent years. This nested setting often requires mark-to-market reevaluation of the portfolio for a large number of possible scenarios of risk factors up to a future time horizon. When closed-form formula is not available, reevaluation may require intensive simulations that are time consuming. This paper aims to develop a new simulation method that is computationally efficient for measurement of conditional Value-at-Risk (CVaR) for the portfolio. We show that CVaR can be represented as the optimal value of an appropriately constructed optimal stopping problem. This result is new to the literature, and opens up the possibility for tackling the problem with existing tools developed for optimal stopping problems that have been studied extensively in the literature. In particular, we propose a lower-bound method based on the well-known least-squares method for optimal stopping. Numerical experiments show that the proposed method produces a very tight lower bound of CVaR for portfolios involving as many as 200 risk factors.